Hot Integral - 33

$PV \int_0^\infty \frac{x^{n-1}}{x^2-3x+2} dx = \pi^a\cot(n\pi)(c-b^{n-1})$

The equation above holds true for positive integers $a$ , $b$ , and $c$ , and $0<n<1$ . Find $ab+bc+ca.$

To clarify, we're asking for the Cauchy principal value of the integral.

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